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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
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Blog Post number 4
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Blog Post number 3
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Blog Post number 2
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Blog Post number 1
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notes
A note of Fourier Analysis
这是关于Stein’s Fourier Analysis的第2, 3, 5, 6章的笔记. 这是一本优雅的教材, 适合学过数学分析的本科生阅读. 笔记补全了书中的一些证明细节, 并覆盖了相关章节中习题所涉及的要点, 可作为阅读原书时的参考.
A note of Differential Equations
这是我学习微分方程引论时的手写课堂笔记. 笔记包含了基本的ODE理论和古典的PDE理论. ODE部分的重点是解方程, 解的延拓, 稳定性和Sturm-Liouville理论. PDE部分的重点是分离变量法, 能量模估计, 极大模原理. 上面提及的重点都是实用且基础的.
A note of Topology
The note is my handwritten note of Topology(H), a very valuable lesson from my point of view. Its content is comprehensive, ranging from point set topology to basic algebraic topology(though Prof.Wang thought it should be called “topological invariant”), even some topics in geometric topology and combinatorial topology. In my opinion, the knowledge about pset topo which has to do with analysis does benefit me a lot, since it can really help you to understand the “skills” in analysis.
A note of Real Analysis
这是我自学实分析时的笔记, 主要参考了Stein’s Real Analysis的前三章和Folland’s Real Analysis的符号测度, 涉及的内容是极其基础的. 初学者应重点掌握MCT, Fatou, DCT, Fubini-Tonelli这四个交换次序的定理, 以及a.e., 测度, L^p这三种收敛模式的关系. 除此之外, 还应掌握LDT, Newton-Leibniz公式, 积分换元和分部积分等实用的知识, 感受实分析的实用之处.
A note of Complex Analysis
这是我自学复分析时的手写笔记, 主要参考了史济怀老师的复变函数和Stein’s Complex Analysis. 复分析课程涉及的主要理论是全纯函数的 Cauchy积分论, Weierstrass级数理论和Riemann映照引出的几何理论. 初学时应感受全纯结构带来的刚性, 进而理解复分析的优美之处. 复分析也是通向几何与数论的桥梁, 若是对数论比较感兴趣, 可以参考Stein’s Complex Analysis第五章后的内容.
A note of Probability Theory and Outer Chapter
这是概率论和概率论进阶的笔记, 主要参考刘党政老师的简明概率论. 内篇为基础的概率论, 从离散型到连续型, 最终证明了大数定律和中心极限定理. 一个极好的参考资料可以在宗语轩学长的主页中找到. 外篇则涉及较多的统计物理内容, 包括随机矩阵, Ising模型, Curie-Weiss模型和李-杨单位圆定理, 其中的随机矩阵部分由于课堂内容过于深刻因此笔记较为简略.
A note of Modern Algebra
这是我学习课程近世代数H时的课堂笔记. 课程从环论自然引入, 以Galois大定理为核心推进, 介绍了基本的代数知识. 在学习中应注意基本例子的积累, 抽象的目的不是为了抽象本身, 而是为了更看得更清楚. 更多的学习资料, 可参考陈小伍老师的课程主页.
A note of Advanced Real Analysis
This note is related to a graduate course Advanced Real Analysis. I mainly refer to Folland’s Real Analysis which is a very classical and comprehensive book.
A note of PDE
This is a note for PDE, especially the start of modern PDE theory. The note mainly concentrate on Sobolev spaces(both the classical and the fractional dimensional), linear elliptic, parabolic and wave equations. Why do I say it’s just the start? Because most of conclusions I mentioned in the note are not surprised from the behaviors of the classical solutions. It is no exaggeration to say that we can just keep the original linear equations in our mind while considering these equtions with a little more complicated forms, since we just assume symmetric matrices for simplification and those lower terms are just not essential.
portfolio
Portfolio item number 1
Short description of portfolio item number 1
Portfolio item number 2
Short description of portfolio item number 2
publications
Paper Title Number 1
Published in Journal 1, 2009
This paper is about the number 1. The number 2 is left for future work.
Recommended citation: Your Name, You. (2009). "Paper Title Number 1." Journal 1. 1(1).
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Paper Title Number 2
Published in Journal 1, 2010
This paper is about the number 2. The number 3 is left for future work.
Recommended citation: Your Name, You. (2010). "Paper Title Number 2." Journal 1. 1(2).
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Paper Title Number 3
Published in Journal 1, 2015
This paper is about the number 3. The number 4 is left for future work.
Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3).
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Paper Title Number 4
Published in GitHub Journal of Bugs, 2024
This paper is about fixing template issue #693.
Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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ta
talks
Talk 1 on Relevant Topic in Your Field
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This is a description of your talk, which is a markdown file that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
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This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.